Hello, my name is Jim and I am a qualified lawyer happy to help you today.
By law, landlords must ensure the property is in good repair under S.11 of the Landlord and Tenant Act 1985.
If they do not, they face prosecution by the local council and can be fined. It would also be breach of contract on their part and you would be within your rights to terminate the tenancy agreement.
The Local Authority Environmental Health Officers have powers under the Housing Act 2004. They have a duty to ensure that properties in their area are in a habitable condition, and will serve improvement notices on landlords of properties which are assessed, under the new Housing Health and Safety Rating System as having ‘category 1 hazards’.
Similar powers are available to Local Authorities under the Environmental Protection Act 1990 if the property is considered a threat to public health.
The presence of mice is a health hazard so really you can tell the landlord you will be moving sooner given the notice period and if they refuse, you will report them to the local council's housing department for all of the issues you have had with the property.
If the landlord and agency maintain their stance then I would recommend that you contact your local council (the housing department).
You can allege breach of contract for the reasons stated above - technically this means you can move out as soon as you want to.
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